Search Results for: dimension

We learn the concepts of a robot’s task space and its configuration space, and the relationship between the dimensions of these two spaces.

We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

What are the consequences of representing a three-dimensional scene using only two-dimensions? The appearance of parallel lines converging and circular objects being elliptical should be surprising but we take this for granted.

Let’s look at how light rays reflected from an object can form an image. We use the simple geometry of a pinhole camera to describe how points in a three-dimensional scene are projected on to a two-dimensional image plane.

We live in a three-dimensional world but it’s taken humans a long time to learn how to realistically depict the illusion of depth on a flat surface.

We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.

We learn how to describe the position and orientation of objects on a 2-dimensional plane. We introduce the notion of reference frames as a basis for describing the position of objects in two dimensions.

Let’s learn how to import a color image into MATLAB and see how the data is organized as a matrix with three dimensions.

The Jacobian matrix provides powerful diagnostics about how well the robot’s configuration is suited to the task. Wrist singularities can be easily detected and the concept of a velocity ellipse is extended to a 3-dimensional velocity ellipsoid.